Derivation of a Closed Expression of the B-S Interaction Kernel for Quark-Antiquark Bound States

The interaction kernel in the Bethe-Salpeter (B-S) equation for quark-antiquark bound states is derivedfrom B-S equations satisfied by the quark-antiquark four-point Green‘s function. The latter equations are establishedbased on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green‘s function andsome other kinds of Green‘s functions, which follow directly from the QCD generating functional. The derived B-Skernel is given by a closed and explicit expression which contains only a few types of Green‘s functions. This expressionis not only convenient for perturbative calculations, but also applicable for nonperturbative investigations. Since thekernel contains all the interactions taking place in the quark-antiquark bound states, it actually appears to be the mostsuitable starting point of studying the QCD nonperturbative effect and quark confinement.     

Lattice Green‘s Function for Infinite Square Lattice in the Second Nearest-Neighbour Interaction Approximation

In dealing with the square lattice model,we replace the traditionally needed Born-Von Karmann periodic boundary condition with additional Hamiltonian terms to make up a ring lattice.In doing so,the lattice Green‘s function of an infinite square lattice in the second nearest-neighbour interaction approximation can be derived by means of the matrix Green‘s function method.It is shown that the density of states may change when the second nearest-neighbour interaction is turned on.``     

Spin-Dependent Transport and Densities of States in Non-collinear Magnetic Barriers

The spin-dependent transport properties in the non-collinear pattern of series of δ-magnetic barriers are studied by using scattering theory and Green‘s function methods. The Green‘s function is obtained by using distorted wave approach and the scattering matrix is related by Fisher-Lee relationship. In addition to reproducing the results of Papp‘s and Xu‘s in parallel and antiparallel configurations, we also obtain further results, where arbitrary orientations of the magnetic barriers and arbitrary number of barriers are included. The main finding of our results is that the signs of polarizations can be switched around some “geometric unpolarized windows“. The well-known antiparallel configuration has no such characteristics. Furthermore, we discuss spin-related partial densities of states in both polarized and unpolarized structures.     

Relativistic Continuum Random Phase Approximation and Applications I. Formalism

A fully consistent relativistic continuum random phase approximation （RCRPA） is constructed in terms of the Green＇s function technique. In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green＇s function, which includes also the negative states in the Dirac sea in the no sea approximation. The theoretical formalism of RCRPA and numerical details are presented. The single particle Green＇s function is calculated numerically by a proper product of regular and irregular solutions of the Dirac equation. The numerical details and the formalism of RCRPA in the momentum representation are presented.     

Nonperturbative Calculation of Shear Viscosity from the Basis of the Keldysh Field in Thermal φ^4 Theory

The nonperturbative result of the shear viscosity in thermal φ^4 theory is given by solving the Bethe-Salpeter (B-S) integral equation in the closed time formalism in real time.By introducing a two-legs-truncated Green function it is shown that the B-S equation is decoupled in the basis of the Keldysh field.     

New Closed Expression of Interaction Kernel in Bethe-Salpeter Equation for Quark-Antiquark Bound States

The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived newly from QCD in the case where the quark and the antiquark are of different flavors. The technique of the derivation is the usage of the irreducible decomposition of the Green‘s functions involved in the Bethe-Salpeter equation satisfied by the quark-antiquark four-point Green‘s function. The interaction kernel derived is given a closed and explicit expression which shows a specific structure of the kernel since the kernel is represented in terms of the quark, antiquark and gluon propagators and some kinds of quark, antiquark and/or gluon three, four, five and six-point vertices. Therefore,the expression of the kernel is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.     

Quantization of electromagnetic field in quadratic continuous nonlinear absorptive dielectrics

This paper reports that in the quantization of electromagnetic field in the dielectrics, the wave equation with regard to the Green function is analytically solved by a direct integral method for a quadratic continuous nonlinear absorptive dielectric medium. The quantization of the electromagnetic field in such a nonlinear absorptive dielectric is carried out for which the material dielectric function is assumed as a separable variable about the frequency and the space coordinate. The vacuum field fluctuations for different spatial continuous variations of dielectric function are numerically calculated, which shows that the present result is self-consistent.     

ACOUSTIC—GRAVITY WAVES CAUSED BY AN IMPULSIVE POINT SOURCE IN THE MIDDLE ATMOSPHERE

In this paper the results of acoustic-gravity wave(AGW)are presented for an impulsive point source inthe middle atmosphere.By virtue of general function theory,the Fourier transformation function is expandedat high frequency and low frequency,respectively.Then Row‘s results are extended from the specialcondition to the general one.When we have cleverly introduced an integral with the parameter,the factor(1/ω_0 t_0)can be obtained,which has a great physical meaning.The conclusion of this paper is as follows:(1)Under special condition the,only has been obtained by approaching ofRow‘s.In the present paper any approaching need not be made in obtaining the results.Besides thethe corrective factor is gained.The less t—α—t_0 is,the more the corrective effect is.(2)Theof formula(12)in Row’s must be corrected to bewhereαis a retardant time(3)(1/ω_0 t_0)~n indicates that when t_0 is greater the corrective effect is less.Also indicates it when T_c islonger the corrective effect is more.(i.e.the lower the     

Isoscalar Giant Monopole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant monopole resonance （ISGMR） in nuclei is studied in the framework of a fully consistent relativistic continuum random phase approximation （RCRPA）. In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green＇s function technique. The negative energy states in the Dirac sea are also included in the single particle Green＇s function in the no-sea approximation. The single particle Green＇s function is calculated numerically by a proper product of the regular and irregular solutions of the Dirac equation. The strength distributions in the RCRPA calculations, the inverse energyweighted sum rule m-1 and the centroid energy of the ISGMR in ^120Sn and ^208Pb are analysed. Numerical results of the RCRPA are checked with the constrained relativistic mean field model and relativistic random phase approximation with a discretized spectrum in the continuum. Good agreement between them is achieved.     

Magnetic Behaviour of Antiferromagnetic Monolayer under an External Field

Magnetic behaviour of antiferromagnetic monolayer under external field is studied. This is the first time to calculate all components of spin statistical average of an anti ferromagnetic system with the random-phase approximation. To do so, a method is developed by many-body Green‘‘s function theory. Magnetization and susceptibility are investigated when external field is applied in either the x- or z-direction. The results are compared with the ferromagnetic monolayer.     

Dipole radiation in the proximity of a chiral slab

Radiation of an electric dipole located along an arbitrary direction in the presence of a chiral slab is formulated using matrix analysis in conjunction with Fourier transform techniques. Moreover, dyadic Green's function of such a structure may be determined for further investigation porpose.     

Electromagnetic volume scattering in the half-space: a moment-method analysis without Sommerfeld integrals or their approximations

Traditionally, in moment-method analyses of electromagnetic scattering, the elements of the impedance matrix are calculated as convolutions of the basis elements with the appropriate dyadic Green's function. However, for scattering in the half-space, the vertical and azimuthal copolar terms of the Green's function require evaluation of Sommerfeld integrals which are computationally burdensome. In this paper, it is shown that, in populating the impedance matrix for the half-space problem, evaluation of Sommerfeld integrals is, in fact, not necessary. For monochromatic excitation, the plane-wave expansion of the scattered field constitutes a Fourier transform, in the horizontal plane, of a vector spectral function. This vector function results from the convolution, in the vertical dimension, of the respective angular spectra of the Green's function and the equivalent current. On application of the moment method, through the Weyl identity, the impedance-matrix elements corresponding to the singular terms of the Green's function are convolutions in the horizontal plane of spherical potentials, and Fourier transforms of scalar spectral functions. These scalar functions are derived from the basis elements and, with a judicious choice of basis, they are well behaved and of compact support, and consequently their Fourier transforms can be computed as FFTs.     

The dyadic Green's function for the cylindrical chirostrip antenna

Using the eigenfunction expansion of dyadic Green's function in unbounded chiral medium, and the method of scattering superposition, the expressions of dyadic Green's function for the one and two—layer cylindrical chirostrip antennas are derived, when the field sources are placed in any layer of cylindrical chirostrip antenna. Also, using the method of saddle point integration, the asymptotic expression of dyadic Green's function for the wraparound chirostrip antenna is obtained. The results can be directly used to analyse the radiation characteristics of cylindrical chirostrip dipolc antenna, et al.     

Retrieval of Green's function and generalized optical theorem for the scattering of complete dyadic fields

Green's function retrieval has been widely used in different research fields due to the fact that the Green's function can be extracted by cross-correlating the records at two receivers. In this paper, the retrieval of the dyadic Green's function is studied by investigating the representation theorem. The generalized optical theorem for the dyadic fields is derived based on the elastic dynamic interferometric equation. By addressing the cross-correlation recorded at two receivers, the important role of the generalized optical theorem and energy equipartition in retrieving the exact Green's function is shown. The presented derivation also shows the Newton-Marchenko equation holdsif the condition of equipartition is not satisfied.     

General approach for finding the characteristics of chiral layered media

In this paper, a systematic approach is presented for finding the resonant frequency, damping factor and EM field distribution of a layered planar structure consisting of chiral media and having arbitrary conductor sheets at the interfaces. The analysis is based on the spectral dyadic Green's function followed by a Ritz-Galerkin's process, using matrix analysis in the Fourier transform spectral domain. The great value of our formulation lies in that it provides methodology for the solutions to chiral layered media problems.     

Fast convergent dyadic Green's function in a rectangular waveguide

Alternative formulas for the dyadic Green's function in a rectangular waveguide are presented. These new functions are deduced by modifying part of Rahmat-Samii's derivation procedures by employing the Poisson summation technique. The Green's function obtained owns fast convergence property and is proved to be more suitable for numerical applications.     

广义Helmholtz方程的Green函数及旋波介质色散关系的另一求解方法

运用并矢法求解广义Helmholtz方程,结合Fourier变换、留数定理等数学处理,给出方程的并矢Green函数解析表达式;并进一步就旋波介质给出其中色散关系的另外一种求解方法．     

On the electromagnetic dyadic Green''s functions for planar multi-layered anistropic uniaxial material media

A complete, plane-wave spectral, vector-wave function expansion of the electromagnetic, electric, and magnetic, dyadic Green's function for electric, as well as magnetic, point currents for a planar, anisotropic uniaxial multi-layered medium is presented. It is given in terms ofz-propagating, source-free vector-wave functions, where is normal to the interfaces, and it is developed via a utilization of the Lorentz reciprocity theorem. The electromagnetic dyadic Green's function for periodic electric as well as magnetic point current sources is also presented. Some salient features of the Green's dyadics, along with a physical interpretation are also described.This work was supported by the IIarry Diamond Laboratories under Contract DAAL02-88-C-0065 with Sabbagh Associates, Inc.     

Improved diagonal tensor approximation (DTA) and hybrid DTA/BCGS-FFT method for accurate simulation of 3D inhomogeneous objects in layered media

This paper presents an improved diagonal tensor approximation (DTA) and its hybridization with the stabilized biconjugate-gradient fast Fourier transform (BCGS-FFT) algorithm to solve a volume integral equation for three-dimensional (3D) objects in layered media. The improvement in DTA is obtained for lossy media through a higher-order approximation. The interaction between the dyadic Green's function and the contrast source is efficiently evaluated by the (FFT) algorithm through the convolution and correlation theorems. For the hybrid implementation, the DTA solution is used as an initial estimate and a preconditioner in the BCGS-FFT algorithm in order to solve the forwards modelling problem accurately with fewer iterations than the conventional BCGS-FFT algorithm. The accuracy and convergence of the DTA, BCGS-FFT and hybrid DTA/BCGS-FFT methods are compared extensively with several numerical examples. Numerical results show that (a) the improved DTA formulation enhances the accuracy and (b) the DTA/BCGS-FFT method can produce results as accurate as the conventional BCGS-FFT but with fewer iterations if the contrast is moderate. For very high contrasts, the hybrid method does not seem to improve further on the BCGS-FFT iteration convergence.     

Suspended stripline on magnetized ferrite and anisotropic dielectric substrates

Suspended stripline on magnetized ferrite and anisotropic dielectric substrates are examined here. The spectral domain immittance approach was used for obtaining the dyadic Green's functions in the Fourier transform domain. Galerkin's method was used to obtain the dispersion characteristics of the dominant mode, and the curves for a few cases are shown as examples which could be used in designing isolators, phase shifters, and directional couplers.